Algebra

Advanced Factorization

Algebraic Identities

         

The polynomial 94x220xy25y29-4x^2-20xy-25y^2 can be factorized as (3+ax+by)(3+cx+dy),(3+ax+by)(3+cx+dy), where a,a, b,b, cc and dd are real numbers. What is the value of abcdabcd?

What is the value of a+b+ca+b+c if x2+8y26xy2yz+zx+4x16y+4z=(xay+b)(xcy+z)?\begin{aligned} & x^2+8y^2-6xy-2yz+zx+4x-16y+4z \\ &= (x-ay+b)(x-cy+z)? \end{aligned}

If aa, bb and cc are real numbers and (x2+2x)279(x2+2x)80=(x+a)2(x+b)(x+c)(x^2+2x)^2-79(x^2+2x)-80=(x+a)^2(x+b)(x+c) is an identity in xx, what is the value of a+b+ca+b+c?

What is the value of a+b+ca+b+c if (x2+3x)2+10x2+30x56=(x1)(x+a)(x2+bx+c)?\begin{aligned} & (x^2+3x)^2+10x^2+30x-56 \\ &= (x-1)(x+a)(x^2+bx+c)? \end{aligned}

What is the value of a+b+ca+b+c if x2+5xy+4y2+5x+23y6=(x+ayb)(x+y+c)?\begin{aligned} & x^2+5xy+4y^2+5x+23y-6 \\ &= (x+ay-b)(x+y+c)? \end{aligned}

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